Equation 23 · Part 8 · What Interpretability Actually Costs to Do at Scale
Starting index or lower bound: i=1
What this part means
This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.
Its job in the formula
i=1 appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Full expression→Starting index or lower bound: i=1→Article meaning
The passage around this formula
A simple model makes the scaling problem legible. Let a verified circuit claim require passing m distinct checks — faithfulness under intervention, completeness against the behavior it is meant to fully explain, minimality against components that turn out not to matter — and let each check take researcher-hours, including the false starts a competent skeptic would force. Total verification cost per claim is . and the field’s own most careful examples put each measured not in minutes but in dedicated researcher-days once ambiguity has to be resolved rather than merely observed. If a frontier model implements even a low four-figure count of distinguishable,…
Learn the underlying idea
Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.
Open the illustrated sums and products: repeat an operation over an index guide →
Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.